# How do you factor 49x^6 – 100y² ?

May 17, 2016

$\left(7 {x}^{3} - 10 y\right) \left(7 {x}^{3} + 10 y\right)$

#### Explanation:

This expression is a $\textcolor{b l u e}{\text{ difference of squares}}$

and In general factors as follows:

$\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{{a}^{2} - {b}^{2} = \left(a - b\right) \left(a + b\right)} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

now $49 {x}^{6} = {\left(7 {x}^{3}\right)}^{2} \text{ and } 100 {y}^{2} = {\left(10 y\right)}^{2}$

$\Rightarrow 49 {x}^{6} - 100 {y}^{2} = {\left(7 {x}^{3}\right)}^{2} - {\left(10 y\right)}^{2} = \left(7 {x}^{3} - 10 y\right) \left(7 {x}^{3} + 10 y\right)$